The results of studying the nuclear spin-lattice relaxation of the nuclear spins of 63,65Cu in the CuAlO2 semiconductor compound (T = 77, 300 K) by the method of nuclear quadrupole resonance of Cu are presented. The relaxation rates in the CuAlO2 compound contain contributions from the magnetic and quadrupole relaxation mechanisms. The magnetic contribution to the relaxation rate is caused by hyperfine magnetic fields of mobile holes. Comparison of the magnetic contribution to the relaxation rate with electrical conductivity made it possible to estimate the carrier concentration and mobility.